Optimal port-based teleportation

Deterministic port-based teleportation (dPBT) protocol is a scheme where a quantum state is guaranteed to be transferred to another system without unitary correction. We characterize the best achievable performance of the dPBT when both the resource state and the measurement is optimized. Surprisingly, the best possible fidelity for an arbitrary number of ports and dimension of the teleported state is given by the largest eigenvalue of a particular matrix -- Teleportation Matrix. It encodes the relationship between a certain set of Young diagrams and emerges as the the optimal solution to the relevant semidefinite program.

[1]  Wen-Chyuan Yueh.  EIGENVALUES OF SEVERAL TRIDIAGONAL MATRICES , 2005 .

[2]  Satoshi Ishizaka,et al.  Asymptotic teleportation scheme as a universal programmable quantum processor. , 2008, Physical review letters.

[3]  Satoshi Ishizaka,et al.  Quantum teleportation scheme by selecting one of multiple output ports , 2009, 0901.2975.

[4]  Michał Horodecki,et al.  Port-based teleportation in arbitrary dimension , 2016, Scientific Reports.

[5]  Joe Harris,et al.  Representation Theory: A First Course , 1991 .

[6]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[7]  Structure and properties of the algebra of partially transposed permutation operators , 2013, 1308.2653.

[8]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[9]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[10]  Commutant structure ofU ⊗(n−1) ⊗U ∗ transformations , 2013 .

[11]  Satoshi Ishizaka,et al.  Some remarks on port-based teleportation , 2015, 1506.01555.

[12]  M. Lewenstein,et al.  Separability and entanglement of composite quantum systems , 1997, quant-ph/9707043.

[13]  Samuel L. Braunstein,et al.  Higher-dimensional performance of port-based teleportation , 2016, Scientific Reports.

[14]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[15]  Salman Beigi,et al.  Simplified instantaneous non-local quantum computation with applications to position-based cryptography , 2011, 1101.1065.

[16]  M. Horodecki,et al.  Commutant structuture of Ux...xUxU* transformations , 2013, 1305.6183.